Transient response of a paper sheet subjected to a travelling thermal pulse: Evolution of temperature, moisture and pressure fields

The response of a paper sheet as it travels through a hot roll nip is of interest in understanding the sheet behavior in photocopiers and laser printers. The fuser section in these devices can often be modeled as a hot roll nip. In this study, the temperature and moisture content fields evolving in two dimensions are calculated by solving the relevant equations of change using finite volume methods. The paper sheet is modeled as a two dimensional porous medium exposed to a thermal pulse moving along the boundary. Allowances for pressure release, mass and heat transfer through the boundary with the surroundings are made. The properties of the paper sheet consisting of the porosity, thermal conductivity, moisture diffusivity and the permeability are assumed to be anisotropic with known components in the z and in-plane directions. The dependence of the moisture equilibrium on temperature is estimated by fitting empirical forms to available sorption data at different temperatures. The temperature and moisture content fields are strongly two-dimensional for typical transit times within the fuser sections of copiers. The penetration of the temperature pulse and the resultant evaporation of moisture depend upon the external conditions including the pulse temperatures, the speed of travel (the residence time in the nip) and the sheet's thermal properties. For typical conditions, simulation results indicate that increasing the nip residence time or the magnitude of the temperature pulse results in more penetration of the temperature fields and more uniform temperature and moisture distributions. These predictions are in broad conformance with experimental observations. The model can be used to study moisture and temperature induced transient mechanical behavior of paper sheets in such configurations where they are subjected to thermal pulses.